Dynamic scaling near the Kasteleyn transition in spin ice: Critical relaxation of monopoles and strings following a field quench

We study dynamics in classical spin ice following a magnetic field quench to close to the Kasteleyn transition, using Monte Carlo simulations and dynamic scaling theory to characterize the relaxation of the magnetization and the density of magnetic monopoles. We have previously argued that this dynamics can be described in terms of seeding and growth of strings of flipped spins, and our results here demonstrate that a solvable stochastic model based on independent strings correctly describes the relaxation as well as the distribution of string lengths within the critical scaling regime near the transition. We also show how generalized scaling forms capture the behavior over a broader range of monopole densities and provide a clear understanding of the breakdown of the scaling picture further from the critical point.